Issue 44

X.-P. Zhou et alii, Frattura ed Integrità Strutturale, 44 (2018) 64-81; DOI: 10.3221/IGF-ESIS.44.06 67 where G 1 is Maxwell shear modulus, G 2 is Kelvin shear modulus,  1 is Maxwell viscosity, and  2 is Kelvin viscosity,          ij ij ij S 11 22 33 ( ) 3 ,          ij ij ij e 11 22 33 ( ) 3 ,        ij i j i j 1 0 ,  ij is stress tensor,  ij is strain tensor. The Maxwell shear modulus is equal to elasticity shear modulus,   ij ij d e e dt 2 2 ,   ij ij de e dt ,   ij ij d S S dt 2 2 ,   ij ij dS S dt . Eq.(5) can be rewritten as                       G t ij ij t e S e G G 2 2 1 1 2 1 1 1 2 2 2 (6) where t is the creep time. From Eq.(6) and works by Yi and Zhu [17], the time factor of the Burgers model under a given load is obtained as                           i iu f t H t G G G f t t t G 1 1 2 1 2 2 ( ) ( ) ( ) 1 1 exp (7) where iu f t ( ) is the time factor for displacement,  i f t ( ) is the time factor for stress,       t H t t 1, 0 ( ) 0, 0 is Heaviside function. According to works by Zhou [18], energy release rate at tips of the mixed mode I- II-III microcracks in Burgers viscoelastic rock matrix can be written as         I II III I II III iu v G t G t G t G t K K K f t E v 2 2 2 2 1 1 ( ) ( ) ( ) ( ) ( ) ( ) 1 (8) where                    iu G G G f t t t G 1 1 2 1 2 2 ( ) 1 1 exp . In Eq. (8), G t ( ) can be rewritten as  iu G t f t G ( ) ( ) (9) where G is energy release rate at tips of the mixed mode I-II-III microcracks in elastic rock matrix. As for the creep fracture, the stress and displacement fields at tips of microcracks can be obtained as follows:          m m m ij ij m m m m i i m K t t K K t u t u K ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (10)